title: Combinatoric analysis of heterogeneous stochastic self-assembly.
abstract: We analyze a fully stochastic model of heterogeneous nucleation and self-assembly in a closed system with a fixed total particle number M, and a fixed number of seeds Ns. Each seed can bind a maximum of N particles. A discrete master equation for the probability distribution of the cluster sizes is derived and the corresponding cluster concentrations are found using kinetic Monte-Carlo simulations in terms of the density of seeds, the total mass, and the maximum cluster size. In the limit of slow detachment, we also find new analytic expressions and recursion relations for the cluster densities at intermediate times and at equilibrium. Our analytic and numerical findings are compared with those obtained from classical mass-action equations and the discrepancies between the two approaches analyzed.
authors.affiliation: Department of Mathematics, CSUN, Los Angeles, California 91330-8313, USA.
authors.forename: Maria R
authors.initials: MR
authors.lastname: D'Orsogna
authors.forename: Bingyu
authors.initials: B
authors.lastname: Zhao
authors.forename: Bijan
authors.initials: B
authors.lastname: Berenji
authors.forename: Tom
authors.initials: T
authors.lastname: Chou
mesh_terms: D000465:Algorithms; D007700:Kinetics; D009010:Monte Carlo Method; D013269:Stochastic Processes